Asymptotics of the system of solutions of a general differential equation with parameter

1996 ◽  
Vol 48 (1) ◽  
pp. 108-121 ◽  
Author(s):  
V. S. Rykhlov
Keyword(s):  
Differential Equation ◽  
General Differential Equation

Existence of conjugate points for self-adjoint linear differential equations

1989 ◽  
Vol 113 (1-2) ◽  
pp. 73-85 ◽  
Author(s):  
Ondřej Došlý
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equations ◽  
Conjugate Points ◽  
General Differential Equation ◽  
Linear Differential

SynopsisThe conjecture of Muller-Pfeiffer [4] concerning the oscillation behaviour of the differential equation (–l)n(p(x)y(n))(n) + q(x)y = 0 is proved, and a similar conjecture concerning the more general differential equation ∑nk=0(−l)k(Pk(x)y(k)(k + q(x)y= 0 is formulated.

A differential equation for undamped forced non-linear oscillations. III

1965 ◽  
Vol 61 (1) ◽  
pp. 133-155 ◽  
Author(s):  
G. R. Morris
Keyword(s):  
Differential Equation ◽  
General Solution ◽  
Periodic Solutions ◽  
Special Interest ◽  
Bounded Solutions ◽  
General Differential Equation ◽  
Dynamical Description ◽  
Image Position ◽  
Essential Problem ◽  
Special Case

The most general differential equation to which the dynamical description of the title applies iswhere dots denote differentiation with respect to t. The essential problem for this equation is to determine the behaviour of solutions as t → ∞. When we attack this problem, the most obvious question is whether, under reasonable conditions on p(t), every solution is bounded as t → ∞ this question is open except when g(x) is linear. In the special case when p(t) is periodic, (1·1) may have periodic solutions; it is clear that any such solution is bounded, and it is worth mentioning that finding periodic solutions is the easiest way of finding particular bounded ones. So long as the bounded-ness problem is unsolved, there is a special interest in finding a large class of particular bounded solutions: if we know such a class then, although we cannot say whether the general solution is bounded or not, we can make the imprecise comment that either the general solution is in fact bounded or the structure of the whole set of solutions is quite complicated.

The Solution of Elastic Stability Problems With the Electric Analog Computer

1959 ◽  
Vol 26 (4) ◽  
pp. 635-642
Author(s):  
J. H. Shields ◽  
R. H. MacNeal
Keyword(s):  
Differential Equation ◽  
Elastic Stability ◽  
Analog Computer ◽  
Computing Methods ◽  
Electrical Circuit ◽  
Stability Problems ◽  
Analog Computing ◽  
General Differential Equation ◽  
Plate Stability ◽  
Electric Analog

Abstract An application of electric analog computing methods to the analysis of elastic stability problems is described. An electrical circuit is first devised which satisfies a general differential equation that is frequently encountered in the literature of elastic stability. This circuit, composed of inductors, capacitors, transformers, and current generators, is then used to obtain solutions for several classical column, framework, and plate-stability problems.

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